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CMPE443 Spring 2009 Assignment Task
Design of a Real-Time System of Manual Control of the Simulated Truck
Motion
The Task
Design and implement a real-time system providing manual control of the simulated motion of a truck.
Mathematical model of the dynamics of a truck and necessary parameters are given in Appendix 1 (see
(4.1)-(4.4), (4.6)-(4.14), Table 1).
It is necessary to implement a program with the following functionalities:
1. Provide user interface via which the parameters of the model can be entered and modified (see
Table 1, the rows with defined values)
2. Provide control means for a driver:
2.1. Start/stop engine work (“on” corresponds to “power supply on”, and “off” – to “power
supply off”. In “on” state, engine torque meets (4.12), (4.13), and in “off”, it is equal to 0. A
pressed button may be used for “on”, and depressed – for “off”)
2.2. Start/stop engine starter (pressed button may be used for “start”, and depressed – for
“stop”, see (4.1), (4.3), (4.4), Table 1, row 22; value of 𝜈 is controlled by the button)
2.3. Connect/disconnect engine from the load using 𝜇 value (a slider may be used to show the
value, see (4.1), (4.2), (4.6) using 𝜇)
2.4. Increase/decrease engine torque (a slider may be used to show the value, see Figure 3.5,
(4.12), (4.13), (4.14))
2.5. Increase/decrease brake torque (a slider may be used to show the value, 𝑀𝑓𝑟:𝜔 ; see Table
1, row 15, (4.11))
Respective values input by the user must be used in the truck model immediately after they are
defined and should affect the next behavior of the truck.
3. Provide output and log of the following information about the current state of the truck
3.1. Angular engine velocity
3.2. Speed of the truck
3.3. Engine torque
3.4. Wheel torque
3.5. Degree of engine-wheel connection (𝜇)
3.6. Current road slope angle
3.7. Brake torque
4. Provide relief of the road (slope angles for different intervals of the road). Total relief length
should be 3 (three) km, and it shall have three 1 km parts with different slopes: 0, negative, and
positive with angles from the range specified in Appendix 1, Table 1, row 21.
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5. Provide graphical output of the dynamic image of the truck moving along the road with the rate
of refreshing of the screen at least 10 times/s
6. The system of two second order ordinary differential equations solution of which gives engine
angular velocity and wheel angular velocity must be solved by any numerical method such as
Euler or fourth order Runge-Kutta methods. Time step should be selected so that with twice
decreased time step solution is practically the same. There should be at least 10 time steps
inside one period of engine revolution.
Report Requirements
Report must contain
1. Assignment may be performed by teams of not greater than 3 people.
2. Each team submits 1 report with the names of participants
3. In the case of team working, in the Introduction to the report there must be explicitly shown
responsibilities of each team’s member (what of the mentioned in “The Task” parts or
combination of them was realized by each person).
4. Printed out report must include: Title (department, course, assignment name, names and ids of
participants, semester, year), Introduction (what for the work is to be done), Task definition
(what must be done, requirements to implementation), Conceptual design (idea of approach,
show parts of the task, their links and interaction), Description of the program implementation
(procedures, interfaces, their interactions), Description of testing (separate testing, integration
process, integrated testing, what examples have you tried, results of testing, screenshots),
Instruction to user (what, where and how should be installed to make your program working),
Conclusion (what was really achieved in comparison with supposed), References to cited sources
if any, Appendix (source codes, diskette with sources and executables, libraries, etc.).
5. Reports submission due date: May 25 (Monday), 2009, 12.00. Hand to Labs Coordinator Mr.
Ghassan Jibril, CMPE-204. REPORTS SUMBITTED LATER WILL BE fined: this day by 5%, and 10%
per each next day of delay.
6. You are to be ready to demonstrate your program and give all necessary explanations on its
work and on the report at the time and place which are to be announced later.
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Appendix 1. Mathematical Model of the Dynamics of a Truck
A schema of a rear-driven vehicular power train consisting of engine and driveline is given in [1, p. 194,
Figure 7.1] and [2, p.24, Figure 4.1].
Subsystems of a vehicular driveline are represented in [1, p. 195, Figure 7.2] and [2, p. 25, Figure 4.2].
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Longitudinal forces acting on a vehicle are shown in [1, p. 196, Figure 7.3] and [2, p. 27, Figure 4.3].
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Let’s consider necessary equations taken from [2] and slightly modified and extended.
External load from the clutch comes in the case when the engine rotating axle is connected to the wheel
via the drive shafts and final drive having gear ratios 𝑖𝑡 and 𝑖𝑓 respectively. It is given by the following
equation (4.2)
1
𝑀𝑐 = 𝜇
𝑀𝑊 ,
(4.2)
𝑖𝑡 𝑖𝑓
where 𝑀𝑊 = 𝐹𝜔 𝑟𝜔 is the wheel torque, and 𝜇 ∈ [0,1] is the degree of the connection of the engine to the
wheel: 𝜇 = 0 for disconnected engine and wheel (neutral gear is engaged), and 𝜇 = 1 for fully connected
case.
At the beginning, when the engine is not rotating,
𝑀𝑚 = 𝑀𝑓𝑟:𝑚 = 𝑀𝑐 = 0,
(4.3)
and to start the engine, a starter, electrical motor, is used:
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𝑀𝑠𝑡𝑎𝑟𝑡𝑒𝑟 = 𝜈𝑀𝑠𝑡𝑎𝑟𝑡 ,
(4.4)
where 𝜈 = 0, when the starter is switched off, and 𝜈 = 1, when the starter is switched on, and 𝑀𝑠𝑡𝑎𝑟𝑡 is the
torque provided by the starter.
𝑀𝜔 = 𝜇(𝑀𝑚 − 𝑀𝑓𝑟:𝑚 )𝑖𝑡 𝑖𝑓 ,
where 𝑖𝑡 and 𝑖𝑓 are gear ratios of the transmission and final drive.
(4.6)
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Variables used in the model (4.1)-(4.4), (4.6)-(4.11) are explained in Table 1 (at the end of the
document).
We consider a vehicle motion in longitudinal direction assuming that it may be inclined upward (positive
𝛼), as in Figure 1, about 40, or downward (negative 𝛼).
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3.14
Figure 1. A truck on the road with the slope angle about 4 ⋅ 180 rad
(http://www.flickr.com/photos/29526939@N03/3421710510/in/pool-old_and_new_trucks_scania/ )
In the model (4.1)-(4.4), (4.6)-(4.11), we have output engine torque 𝑀𝑒 = 𝑀𝑚 − 𝑀𝑓𝑟:𝑚 resulting from
the combustion of the supplied fuel and the internal friction of the engine. A driver can accelerate the
truck by increase of the torque 𝑀𝑒 , that depends on the current rotational velocity 𝜃̇𝑚 = 2𝜋𝑛 (𝑛 is the
frequency of rotation in Herz) of the engine flywheel. Dependency of the maximal torque 𝑀𝑒 on the
rotational velocity of the engine flywheel (in revolutions per minute, RPM) is given in the [2, p. 17,
Figure 3.5] for two types of diesel engines:
We assume that actual torque of the engine is in the range
1
𝑇
(𝜃̇ ), 𝑇𝑒𝑚𝑎𝑥 (𝜃̇𝑚 )],
100 𝑒𝑚𝑎𝑥 𝑚
𝑇𝑒 (𝜃̇𝑚 ) ∈ [
(4.12)
where 𝑇𝑒𝑚𝑎𝑥 (𝜃̇𝑚 ) is the maximal torque produced by the engine at the angular velocity 𝜃̇𝑚 and may be
obtained from the graphics as shown in Figure 3.5. The engine falls down when the angular velocity is
below the minimal angular velocity or exceeds the maximal angular velocity shown in such graphics (for
Figure 3.5, rotational velocity of the engines must be inside the interval [1000RPM, 2000RPM]). Let’s
consider DSC12 engine. Extending the graphic to the left (less than 1000RPM), we get by linear
extrapolation, using 𝑇𝑒𝑚𝑎𝑥 (1000) = 1800, 𝑇𝑒𝑚𝑎𝑥 (0) = 0 , and representing angular velocity in RPM.
𝑇𝑒𝑚𝑎𝑥 (𝜃̇𝑚 ) =
𝑇𝑒𝑚𝑎𝑥 (1000)−𝑇𝑒𝑚𝑎𝑥 (0)
(𝜃̇𝑚
1000−0
− 0) + 𝑇𝑒𝑚𝑎𝑥 (0) = 1.8𝜃̇𝑚
(4.13)
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We used in (4.13) the fact that the torque produced by a not rotating engine is equal to zero.
Hence, at first, the engine must be switched on. It is made by the starter (electrical motor), providing the
initial torque to the engine flywheel having initially
𝜃𝑚 (0) = 𝜃̇𝑚 (0) = 0 .
(4.14)
Starting of the engine is made with the neutral gear engaged (𝜇 = 0). When the engine starts rotation, it
produces the torque which is used for the further increase of the engine rotation, and its value can be
controlled by the driver using (4.12).
Then, after the engine angular velocity is in the range shown in Figure 3.5, the load can be connected to
the engine by increasing of 𝜇 from 0 to 1 gradually.
To decelerate, brakes producing decelerating torque 𝑀𝑓𝑟:𝜔 are used.
We consider a Scania 144L 6x2 truck with DSC12 engine. Parameters of the truck and engine are given in
Table 1.
References
1. U. Kiencke, L. Nielsen, Automotive Control Systems. For Engine, Driveline, and Vehicle. 2nd Ed.,
Springer-Verlag, Berlin, 2005, 512 p., ISBN 3-540-23139-0, available at EMU Library, pp. 193-201.
2. M. Pettersson, Driveline Modeling and Control, Linkoping Studies in Science and Technology,
Dissertation No. 484, Department of Electrical Engineering, Linkoping University, Sweden, 1997,
www.vehicular.isy.liu.se/Publications/PhD/97-484-MP.pdf, 97-484-MPetersson.pdf
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Table 1. Variables used in the model (4.1)-(4.4), (4.6)-(4.11) and their values to be used in the simulation
No
1.
2.
Variable Value to be used (if
name
a range ,[a,b], is
shown, use the
maximal value, b)
𝐽𝜔
6
𝑚
24000
Dimension Explanation
𝑘𝑔 ⋅ 𝑚2
𝑘𝑔
3.
4.
5.
𝑟𝜔
𝑖𝑡
𝑖𝑓
0.3
[1,6]
[1,10]
𝑚
6.
𝐽𝑚
[0.15,0.3]
𝑘𝑔 ⋅ 𝑚2
7.
𝜃̇𝜔
8.
9.
𝑣
= 𝜃̇𝜔 𝑟𝜔
𝑀𝑚
10.
11.
𝑀𝑓𝑟:𝑚
𝑀𝑐
12.
13.
𝑀𝑊
𝜇
14.
𝑀𝜔
15.
𝑀𝑓𝑟:𝜔
≤ 3000
𝑁⋅𝑚
16.
𝑐𝑟1 , 𝑐𝑟2
𝑐𝑟1
∈ [0.03, 0.035], 𝑐𝑟2
∈ [0.006, 0.0075]
𝑚 1
,
𝑠2 𝑠
≤ 1900 (see
Figure 3.5)
0
𝑟𝑎𝑑
𝑠
𝑚
𝑠
𝑁⋅𝑚
𝑁⋅𝑚
𝑁⋅𝑚
𝑁⋅𝑚
[0,1]
𝑁⋅𝑚
The mass moment of inertia of the wheel (see (4.10))
The full mass of the truck considered at the Center of Gravity
(CoG) (see (4.7))
The wheel radius (see (4.10))
The transmission gear conversion ratio (see (4.6))
The final drive gear conversion ratio (see (4.6)). Maximal 𝑖𝑡 𝑖𝑓
value is 60 according to [1, p. 204].
The mass moment of inertia of the engine (see (4.1)). Limits are
according to [1, p. 122]
The wheel rotational speed (it is the first derivative of the angle
of the wheel rotation) (see (4.10))
The speed of the truck CoG (see (4.7) and (4.11))
The output torque of the engine (see (4.1))
The torque of the internal friction from the engine (see (4.1))
The torque from the external load from the clutch on the
engine flywheel (see (4.1), (4.2))
The torque produced by the rotating wheel (see (4.2), (4.7))
The degree of the engine and wheel connection (see (4.2) and
(4.6))
The accelerating torque produced by engine and transmitted to
the wheel (see (4.6) and (4.11))
The decelerating torque produced by the brakes when the
brake pedal is pressed (see (4.11))
The coefficients defining the wheel rolling resistance force (see
(4.9)) According to
http://en.wikipedia.org/wiki/Rolling_resistance,
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No
Variable Value to be used (if
name
a range ,[a,b], is
shown, use the
maximal value, b)
Dimension Explanation
17.
𝑐𝑎𝑖𝑟
[0.6,1]
18.
𝐴𝑎
3.2 ⋅ 2.5 = 8
𝑚2
19.
𝜌𝑎
1.2
20.
𝑔
9.81
21.
22.
𝛼
𝑀𝑠𝑡𝑎𝑟𝑡
[−0.3,0.3]
3
𝑘𝑔
𝑚3
𝑚
𝑠2
𝑟𝑎𝑑
𝑁⋅𝑚
www.cvdc.org/recent_papers/PopovColeCebonWinkler.pdf
The drag coefficient (see (4.8)). Range according to
http://www.bgsoflex.com/airdragchart.html
The maximum vehicle cross section area (see (4.8)). Height=3.5
m, width=2.5 m, length=6 m
The air density (see (4.8))
The gravitational acceleration, a constant (see (4.7))
The slope of the road (see (4.7))
The torque provided by the switched on starter